In this paper, a modified normalized Rortex/vortex identification method named Omega_R is presented to improve the original Omega_R method and cure the bulging phenomenon on the iso-surfaces caused by the original Omega_R method. Detailed mathematical explanations and the relationship with the Q criterion are described. In addition, the new developed formula does not require two original coordinate rotations, and the calculation is greatly simplified. The numerical results are demonstrated to show the effectiveness of the new modified normalized Rortex/vortex identification method.

Letter: Modified normalized Rortex/vortex identification method.

In this paper, a modified normalized Rortex/vortex identification method named ΩR is presented to improve the original ΩR method and resolve the bulging phenomenon on the isosurfaces, which is caused by the original ΩR method. Mathematical explanations and the relationship between the Q criterion and ΩR are described in detail. In addition, the new developed formula does not require two original coordinate rotations, and the calculation of ΩR is greatly simplified. The numerical results demonstrate the effectiveness of the new modified normalized Rortex/vortex identification method.In this paper, a modified normalized Rortex/vortex identification method named ΩR is presented to improve the original ΩR method and resolve the bulging phenomenon on the isosurfaces, which is caused by the original ΩR method. Mathematical explanations and the relationship between the Q criterion and ΩR are described in detail. In addition, the new developed formula does not require two original coordinate rotations, and the calculation of ΩR is greatly simplified. The numerical results demonstrate the effectiveness of the new modified normalized Rortex/vortex identification method.

Modified normalized Rortex/vortex identification method

Experimental and numerical investigation of ventilated cavitating flow structures with special emphasis on vortex shedding dynamics

Numerical modelling of unsteady cavitation and induced noise around a marine propeller

The flow structure and the unsteady mechanism of the unsteady cavitating flow are reviewed in this paper. The flow patterns and structures in different cavitation regime, for the attached cavitation and the vortical cavitation, are shown with both the visualization and the quantitative information. The attached cavitating flow around the Clark-Y hydrofoil and the vortical cavitating flow around the Tulin hydrofoil are considered. In particular, the phenomena such as the large-scale vortex structure and the re-entrant flow associated with the cloud cavitation, and the cavitating vortex street’s forming and crumbling are described. The evolution of the cavitation structure in the transient sheet/cloud cavity forming, along with the cavity collapse induced by the re-entrant flow and the shock wave propagation are discussed. The perspective future research of higher fidelity simulations, and the accurate identifications of the cavitating vortex structure is commented.

A review of transient flow structure and unsteady mechanism of cavitating flow

Unsteady pressure fluctuation characteristics in the process of breakup and shedding of sheet/cloud cavitation

Numerical investigation of cavitation vortex dynamics in unsteady cavitating flow with shock wave propagation

Cavitation is a complex multiphase flow phenomenon with an abrupt transient phase change between the liquid and the vapor, including multiscale vortical motions. The transient cavitation dynamics is closely associated with the evolution of the cavitation vortex structures. The present paper investigates the cavitation vortex dynamics using different vortex identification methods, including the vorticity method, the Q criterion method, the Omega method (Ω), the λ2 method and the Rortex method. The Q criterion is an eigenvalue-based criterion, and in the Omega method, the parameter is normalized, is independent of the threshold value and in most conditions Ω=0.52. The Rortex method is based on an eigenvector-based criterion. Numerical simulations are conducted using the implemented compressible cavitation solver in the open source software OpenFOAM for the sheet/cloud cavitating flows around a NACA66 (mod) hydrofoil fixed at α=6°, σ=1.25 and Re=7.96×105. The flow is characterized by the alternate interactions of the re-entrant flow and the collapse induced shock wave. Results include the vapor structures and the vortex dynamics in the unsteady sheet/cloud cavitating flows, with emphasis on the vortex structures in the cavitation region, the cavity interface, the cavity closure, the cavity wakes, and the foil wakes with the shedding cavity. The comparisons of the various methods, including that the vorticity method, the Q criterion method, the Omega method, the λ2 method and the Rortex method, show the performances of different methods in identifying the cavitation vortex structures. Generally, during the attached cavity growth stage, the Q criteria can well predict the vortex structures in the cavitation region and at the foil trailing edge in the pure liquid region, while with the Omega method and the Rortex method, the vortex structures outside the attached cavity and on the foil pressure side can also be predicted. The λ2 method can well predict the vortex structures in the cavity closure region. During the re-entrant jet development stage, the vortex structures in the re-entrant jet region is weak. During the cavity cloud shedding stage, the vortex dynamics at the foil leading edge covered by newly grown cavity sheet is different from that during the attached cavity sheet growth stage. During the shock wave formation and propagation stage, strong vortex structures with both the size and the strength are observed owing to the cavity cloud shedding and collapse behavior. The influence of the small parameter e in the Omega method on the cavitation vortex identification is discussed.

Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods

The objective of this paper is to investigate the unsteady cavitation behaviors and the corresponding cavitating flow-induced vibrations. Results are presented for the modified NACA66 hydrofoils made of stainless steel and POM Polyacetate respectively at Re = 6.0×105 for various cavitation regimes. The high-speed camera and the single point laser Doppler vibrometer (LDV) are used to observe the transient cavitating flow patterns and measure the vibration velocities. The results showed that the vibration amplitude increases dramatically for the cloud cavitation due to the development of large-scale cloud cavity. The main flow-induced frequencies, which are in accordance with the cavity shedding frequency, decrease with the decrease of the cavitation number. As for the effect of the hydroelastic response on the vibration behavior, the lift coefficient for the POM Polyacetate hydrofoil fluctuates more significantly with a larger mean value than that for the stainless steel hydrofoil. Compared with the vaporous cavity along the suction side of the stainless steel hydrofoil, the cavity for POM Polyacetate hydrofoil appears to be fragmentized. The main vibration frequencies for the POM Polyacetate hydrofoil are larger than that for the stainless steel hydrofoil, with the chaotic hydroelastic response with high frequency.

Wang Changchang

Papers

Unsteady pressure fluctuation characteristics in the process of breakup and shedding of sheet/cloud cavitation

Numerical investigation of cavitation vortex dynamics in unsteady cavitating flow with shock wave propagation

Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods

Measurement and prediction of cavitating flow-induced vibrations

Characteristics and dynamics of compressible cavitating flows with special emphasis on compressibility effects